The asymmetric division of the one-cell Caenorhabditis elegans zygote gives rise to two cells of different size and fate, thereby establishing the animal's anterior--posterior (a-p) axis. Through genetics, a number of genes required for this polarity have been characterized, but many components remain unidentified. Recently, our laboratory discovered a mutation in the pod-1 gene (for polarity a...

The Proper Orthogonal Decomposition (POD) uses data to generate an optimal set of basis functions that represent the " energy " of the data, defined by a user-selected norm. This basis is optimal in the sense that a finite number of these modes represent more of the energy than any other set of orthogonal modes. The POD can be seen, on one hand, as a way to define energetic structures in a flow...

We propose a framework for dynamic mode decomposition of 2D flows, when numerical or experimental data snapshots are captured with large time steps. Such problems originate for instance from meteorology, when a large time step acts like a filter in obtaining the significant Koopman modes, therefore the classic dynamic mode decomposition method is not effective. This study is motivated by the ne...

The hydrodynamics of a highly deformable fish pectoral fin used by a bluegill sunfish (Lepomis macrochirus) during steady forward swimming are examined in detail. Lowdimensional models of the fin gait based on proper orthogonal decomposition (POD) are developed, and these are subjected to analysis using an incompressible Navier– Stokes flow solver. The approach adopted here is primarily motivat...

Reduced-order models of the nonlinear Complex Ginzburg-Landau (CGL) equation are computed using a nonlinear generalization of balanced truncation. The method involves Galerkin projection of the nonlinear dynamics onto modes determined by balanced truncation of a linearized system, and is compared to a standard method using projection onto Proper Orthogonal Decomposition (POD) modes computed fro...

We develop low-dimensional models for the evolution of a free shear layer in a periodic domain. The goal is to obtain models simple enough to be analyzed using standard tools from dynamical systems theory, yet including enough of the physics to model nonlinear saturation and energy transfer between modes (e.g., pairing). Recently, experiments have suggested that high-frequency forcing of shear ...

The Proper Orthogonal Decomposition (POD) is a method that may be applied to linear and nonlinear structures for extracting important information from a measured structural response. Previous methods of using the POD for system identification typically use the POD for model reduction only and system identification is accomplished via standard methods. A method for using the POD-based identifica...

We investigate nonlinear dynamical models for selfsustained oscillations in the flow past a rectangular cavity. The models are based on the method of Proper Orthogonal Decomposition (POD) and Galerkin projection, and we introduce an inner product and formulation of the equations of motion which enables one to use vector-valued POD modes for compressible flows. We obtain models between 3 and 20 ...

In this article, an improved reduced order modelling approach, based on the proper orthogonal decomposition (POD) method, is presented. After projecting the governing equations of flow dynamics along the POD modes, a dynamical system was obtained. Normally, the classical reduced order models do not predict accurate time variations of flow variables due to some reasons. The response of the dynam...